Summative assessment data are rarely adapted into instructional decision making. In this project, teachers and researchers work together to identify how teachers use diagnostic data (students' development of common core standards). We analysed students' responses to trimester tests that teachers and researchers modified together using cognitive…

The purpose of this work was to explore how elementary pre-service' teachers (PSTs) responded to a volume task that asked for a coordination of changes in one dimension with changes in volume. We carried out both written pre-assessments and follow-up interviews with seventeen PSTs, focused on exploring volume content knowledge. Our findings…

The purpose of this work was to explore how elementary pre-service teachers responded to a novel strategy for justifying the triangle area formula. We conducted interviews with 24 pre-service teachers, asking them to evaluate and respond to a hypothetical student strategy for the triangle area. Findings highlighted several interesting struggles…

In this article, we describe one possible way to modify volume tasks in textbooks to promote conceptual understanding of the volume formula: length × width × height. From the results of previous studies regarding students' understanding of volume measurement, we identified three conceptual ideas key to understanding volume: filling…

In this study, we examined five limit lessons using Mathematical Tasks Framework to understand students' opportunities to learn cognitively challenging tasks and maintain cognitive demand during limit lessons. Our analysis of Dr A's five lessons shows that students rarely had opportunities to maintain or increase cognitive demand. There are two…

This paper compares sections on functions and linear functions from two Korean textbooks and an American standards-based textbook (University of Chicago School Mathematics Project [UCSMP] Algebra) to understand differences and similarities among these textbooks through horizontal and vertical analyses. We found that these textbooks provide…

In its mathematics standards, National Council of Teachers of Mathematics (NCTM) states that problem solving is an integral part of all mathematics learning and exposure to problem solving strategies should be embedded across the curriculum. Furthermore, by high school, students should be able to use, decide and invent a wide range of strategies.…

In this study, we analyzed and compared reasoning and proving opportunities in geometry lessons from American standard-based textbooks and Korean textbooks to understand how these textbooks provide student opportunities to engage in reasoning and proving activities. Overall, around 40% of exercise problems in Core Plus Mathematics Project (CPMP)…

In this study, we examined 10 integral lessons to understand students' opportunities to learn cognitively challenging tasks and maintain cognitive demand during integral lessons. Our findings reveal issues with implemented tasks as well as the way these tasks were presented to students. We also examined mathematicians' reasons behind their…